Multiplicity (mathematics)
In math, multiplicity means how many times a specific number appears as a solution to an equation.
For example, let's say we have the equation (x-2)(x+3)(x-2) = 0.
To solve for x, we need to figure out which numbers make the equation equal to zero. We can see that x=2 and x=-3 are solutions because if we substitute them into the equation, the entire equation equals zero.
However, notice how x=2 appears twice in the equation, and x=-3 only appears once. We say that x=2 has a multiplicity of 2, and x=-3 has a multiplicity of 1.
What this means is that when we graph the equation, x=2 will show up as a "bump" or a "hill" on the graph since it appears twice, while x=-3 will show up as just a regular point.
So, multiplicity is all about counting how many times a specific number shows up in an equation as a solution.
For example, let's say we have the equation (x-2)(x+3)(x-2) = 0.
To solve for x, we need to figure out which numbers make the equation equal to zero. We can see that x=2 and x=-3 are solutions because if we substitute them into the equation, the entire equation equals zero.
However, notice how x=2 appears twice in the equation, and x=-3 only appears once. We say that x=2 has a multiplicity of 2, and x=-3 has a multiplicity of 1.
What this means is that when we graph the equation, x=2 will show up as a "bump" or a "hill" on the graph since it appears twice, while x=-3 will show up as just a regular point.
So, multiplicity is all about counting how many times a specific number shows up in an equation as a solution.